I've been playing with spreadsheets that have formulae with logs in them. Certain of these spreadsheets effectively approximate logs by summing the inverses of something being counted. So, what I'm *really* doing in these spreadsheets is computing harmonic series. The problem is, the approximation of the standard harmonic series to a log function isn't very good. So, still using a spreadsheet, how can we fiddle with the formulae to better approximate a log function? Idea #1. sum(1/(i+fudge),i,1,n), where fudge is some small constant to be determined. Is there an "optimal" value of fudge that minimizes the error under some error model ? Idea #2. sum(1/(i+fudge[i]),i,1,n), where fudge[i] is an array of small (|fudge[i]|<1) constants that "sample" the function 1/x at somewhat more optimum points ? Any other ideas?